Question

(6n-1)^2+2(6n-1)-80=0 n=??

Answer 1

Lets do variable substitution. Let x = 6n-1. Then your equation becomes:
\[x^{2} +2x-80 = 0\]
This factors nicely:
\[(x-8)(x+10) = 0\]
So x = 8 and x = -10
Now to put back out substitution:
6n -1 = 8 means n = 3/2
6n-1 = -10 means n = -3/2

Answer 2

wow! thank you! we haven't even learned about variable substitution but i like it!